盛万成,王 斌.Van der Waals气体Euler方程的Riemann问题及基本波的相互作用[J].数学年刊A辑,2016,37(4):377~396
Van der Waals气体Euler方程的Riemann问题及基本波的相互作用
Riemann Problem and Interaction of Elementary Waves to the Euler Equations for Van der Waals Gas
Received: May 17, 2015  Revised: February 04, 2016
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中文关键词:  Euler方程, Van der Waals气体, Riemann问题, 基本波的相互作用
英文关键词:Euler equations, Van der Waals gas, Riemann problem, Interaction of elementary waves
基金项目:本文受到国家自然科学基金 (No.11371240)的资助.
Author NameAffiliation
SHENG Wancheng Corresponding author. College of Sciences, Shanghai University, Shanghai 200444, China. 
WANG Bin College of Sciences, Shanghai University, Shanghai 200444, China. 
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中文摘要:
      研究了修正的等熵Van der Waals气体动力学Euler方程~Riemann 问题及其基本波的相互作用. 利用Maxwell提出的等面积法则, 将 Van der Waals气体状态方程修正为与实际相符, 从而守恒律方程组从混合型转化为双曲型. 利用广义特征线分析法, 构造性地得到了~Riemann~问题的解是存在的. 进一步, 得到了基本波相互作用.
英文摘要:
      This paper deals with the Riemann problem for the Euler equations and the interaction of elementary waves for isentropic modified Van der Waals gas. The authors modify the state equation of Van der Waals gas to agree with the reality by the area equal principle, which Maxwell constructed. Then the system is transformed from mixed type into hyperbolic type. By the characteristic analysis methods, the authors get the Riemann solutions constructively. Furthermore, the collisions of shock and another elementary waves are shown.
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